Search NASA⌕ Search

SEARCH · Search NASA

Results for “Density function theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Basic principles and recent observations of rotationally sampled wind

The concept of rotationally sampled wind speed is described. The unusual wind characteristics that result from rotationally sampling the wind are shown first for early measurements made using an 8-point ring of anemometers on a vertical plane array of meteorological towers. Quantitative characterization of the rotationally sampled wind is made in terms of the power spectral density function of the wind speed. Verification of the importance of the new concept is demonstrated with spectral analyses of the response of the MOD-OA blade flapwise root bending moment and the corresponding rotational analysis of the wind measured immediately upwind of the MOD-OA using a 12-point ring of anemometers on a 7-tower vertical plane array. The Pacific Northwest Laboratory (PNL) theory of the rotationally sampled wind speed power spectral density function is tested successfully against the wind spectrum measured at the MOD-OA vertical plane array. A single-tower empirical model of the rotationally sampled wind speed is also successfully tested against the measurements from the full vertical plane array. Rotational measurements of the wind velocity with hotfilm anemometers attached to rotating blades are shown to be accurate and practical for research on winds at the blades of wind turbines. Some measurements at the rotor blade of a MOD-2 turbine using the hotfilm technique in a pilot research program are shown. They are compared and contrasted to the expectations based upon application of the PNL theory of rotationally sampled wind to the MOD-2 size and rotation rate but without teeter, blade bending, or rotor induction accounted for. Finally, the importance of temperature layering and of wind modifications due to flow over complex terrain is demonstrated by the use of hotfilm anemometer data, and meteorological tower and acoustic doppler sounder data from the MOD-2 site at Goodnoe Hills, Washington.

Connell, James R.↗
NASA NTRS1975

High zonal harmonics of rapidly rotating planets

A new perturbation expansion is derived for the structure of rotating bodies in hydrostatic equilibrium. The method uses an expansion of the density on Legendre polynomial functions of angle, and can be developed analytically in a manner analogous to the standard level-surface perturbation theory. The new theory proceeds from a prescribed pressure-density relation rather than from a prescribed density distribution, and is both simpler and more physically transparent than the level-surface approach. High zonal harmonics are shown to arise via a transfer function involving derivatives of the interior sound velocity, and via mixing of multipole density components in the outer shell of the planet. Sample calculations for polytropic sequences are presented, as well as standard gravity models for Jupiter and Saturn. Mathematical subleties of the theory are discussed in an appendix.

Hubbard, W. B.↗
NASA NTRS1979

The applicability of Brillouin scattering to flow field diagnostics

To fill the void between turbulence theory and experiment; particularly in the flow fields consisting of monatomic gases, for example in wind tunnels, means of measuring fluctuating quantities are needed. In the area of density fluctuation measurement, the optical method of Brillouin scattering was suggested. This was based on the theory, that the Brillouin scattered intensity is proportional to a function of density. In this investigation the potential of this method as a diagnostic tool was studied. Here the density fluctuations in gases were sought. Continuous wave lasers and interferometers were used as the primary illuminating source and scattered light filters respectively.

Laiosa, J.↗
NASA NTRS1974

An improved exceedance theory for combined random stresses

An extension is presented of Rice's classic solution for the exceedances of a constant level by a single random process to its counterpart for an n-dimensional vector process. An interaction boundary, analogous to the constant level considered by Rice for the one-dimensional case, is assumed in the form of a hypersurface. The theory for the numbers of boundary exceedances is developed by using a joint statistical approach which fully accounts for all cross-correlation effects. An exact expression is derived for the n-dimensional exceedance density function, which is valid for an arbitrary interaction boundary. For application to biaxial states of combined random stress, the general theory is reduced to the two-dimensional case. An elliptical stress interaction boundary is assumed and the exact expression for the density function is presented. The equations are expressed in a format which facilitates calculating the exceedances by numerically evaluating a line integral. The behavior of the density function for the two-dimensional case is briefly discussed.

Lester, H. C.↗
NASA NTRS1975

A sequential nonparametric pattern classification algorithm based on the Wald SPRT

A sequential nonparametric pattern classification procedure is presented. The method presented is an estimated version of the Wald sequential probability ratio test (SPRT). This method utilizes density function estimates, and the density estimate used is discussed, including a proof of convergence in probability of the estimate to the true density function. The classification procedure proposed makes use of the theory of order statistics, and estimates of the probabilities of misclassification are given. The procedure was tested on discriminating between two classes of Gaussian samples and on discriminating between two kinds of electroencephalogram (EEG) responses.

Poage, J. L.↗
NASA NTRS1999

Structural Reliability Analysis and Optimization: Use of Approximations

This report is intended for the demonstration of function approximation concepts and their applicability in reliability analysis and design. Particularly, approximations in the calculation of the safety index, failure probability and structural optimization (modification of design variables) are developed. With this scope in mind, extensive details on probability theory are avoided. Definitions relevant to the stated objectives have been taken from standard text books. The idea of function approximations is to minimize the repetitive use of computationally intensive calculations by replacing them with simpler closed-form equations, which could be nonlinear. Typically, the approximations provide good accuracy around the points where they are constructed, and they need to be periodically updated to extend their utility. There are approximations in calculating the failure probability of a limit state function. The first one, which is most commonly discussed, is how the limit state is approximated at the design point. Most of the time this could be a first-order Taylor series expansion, also known as the First Order Reliability Method (FORM), or a second-order Taylor series expansion (paraboloid), also known as the Second Order Reliability Method (SORM). From the computational procedure point of view, this step comes after the design point identification; however, the order of approximation for the probability of failure calculation is discussed first, and it is denoted by either FORM or SORM. The other approximation of interest is how the design point, or the most probable failure point (MPP), is identified. For iteratively finding this point, again the limit state is approximated. The accuracy and efficiency of the approximations make the search process quite practical for analysis intensive approaches such as the finite element methods; therefore, the crux of this research is to develop excellent approximations for MPP identification and also different approximations including the higher-order reliability methods (HORM) for representing the failure surface. This report is divided into several parts to emphasize different segments of the structural reliability analysis and design. Broadly, it consists of mathematical foundations, methods and applications. Chapter I discusses the fundamental definitions of the probability theory, which are mostly available in standard text books. Probability density function descriptions relevant to this work are addressed. In Chapter 2, the concept and utility of function approximation are discussed for a general application in engineering analysis. Various forms of function representations and the latest developments in nonlinear adaptive approximations are presented with comparison studies. Research work accomplished in reliability analysis is presented in Chapter 3. First, the definition of safety index and most probable point of failure are introduced. Efficient ways of computing the safety index with a fewer number of iterations is emphasized. In chapter 4, the probability of failure prediction is presented using first-order, second-order and higher-order methods. System reliability methods are discussed in chapter 5. Chapter 6 presents optimization techniques for the modification and redistribution of structural sizes for improving the structural reliability. The report also contains several appendices on probability parameters.

Grandhi, Ramana V.↗
NASA NTRS1981

Electron-beam-charged dielectrics: Internal charge distribution

Theoretical calculations of an electron transport model of the charging of dielectrics due to electron bombardment are compared to measurements of internal charge distributions. The emphasis is on the distribution of Teflon. The position of the charge centroid as a function of time is not monotonic. It first moves deeper into the material and then moves back near to the surface. In most time regimes of interest, the charge distribution is not unimodal, but instead has two peaks. The location of the centroid near saturation is a function of the incident current density. While the qualitative comparison of theory and experiment are reasonable, quantitative comparison shows discrepancies of as much as a factor of two.

Beers, B. L.↗
NASA NTRS1991

Electronic structure Fermi liquid theory of high Tc superconductors: Comparison of predictions with experiments

Predictions of local density functional (LDF) calculations of the electronic structure and transport properties of high T(sub c) superconductors are presented. As evidenced by the excellent agreement with both photoemission and positron annihilation experiments, a Fermi liquid nature of the 'normal' state of the high T(sub c) superconductors become clear for the metallic phase of these oxides. In addition, LDF predictions on the normal state transport properties are qualitatively in agreement with experiments on single crystals. It is emphasized that the signs of the Hall coefficients for the high T(sub c) superconductors are not consistent with the types of dopants (e.g., electron-doped or hole-doped) but are determined by the topology of the Fermi surfaces obtained from the LDF calculations.

Yu, Jaejun↗
NASA NTRS1996

Electromagnetic Compatibility Testing Studies

This report discusses the results on analytical models and measurement and simulation of statistical properties from a study of microwave reverberation (mode-stirred) chambers performed at Texas Tech University. Two analytical models of power transfer vs. frequency in a chamber, one for antenna-to-antenna transfer and the other for antenna to D-dot sensor, were experimentally validated in our chamber. Two examples are presented of the measurement and calculation of chamber Q, one for each of the models. Measurements of EM power density validate a theoretical probability distribution on and away from the chamber walls and also yield a distribution with larger standard deviation at frequencies below the range of validity of the theory. Measurements of EM power density at pairs of points which validate a theoretical spatial correlation function on the chamber walls and also yield a correlation function with larger correlation length, R(sub corr), at frequencies below the range of validity of the theory. A numerical simulation, employing a rectangular cavity with a moving wall shows agreement with the measurements. The determination that the lowest frequency at which the theoretical spatial correlation function is valid in our chamber is considerably higher than the lowest frequency recommended by current guidelines for utilizing reverberation chambers in EMC testing. Two suggestions have been made for future studies related to EMC testing.

Trost, Thomas F.↗
NASA NTRS2000

Optical Performance Modeling of FUSE Telescope Mirror

We describe the Metrology Data Processor (METDAT), the Optical Surface Analysis Code (OSAC), and their application to the image evaluation of the Far Ultraviolet Spectroscopic Explorer (FUSE) mirrors. The FUSE instrument - designed and developed by the Johns Hopkins University and launched in June 1999 is an astrophysics satellite which provides high resolution spectra (lambda/Delta(lambda) = 20,000 - 25,000) in the wavelength region from 90.5 to 118.7 nm The FUSE instrument is comprised of four co-aligned, normal incidence, off-axis parabolic mirrors, four Rowland circle spectrograph channels with holographic gratings, and delay line microchannel plate detectors. The OSAC code provides a comprehensive analysis of optical system performance, including the effects of optical surface misalignments, low spatial frequency deformations described by discrete polynomial terms, mid- and high-spatial frequency deformations (surface roughness), and diffraction due to the finite size of the aperture. Both normal incidence (traditionally infrared, visible, and near ultraviolet mirror systems) and grazing incidence (x-ray mirror systems) systems can be analyzed. The code also properly accounts for reflectance losses on the mirror surfaces. Low frequency surface errors are described in OSAC by using Zernike polynomials for normal incidence mirrors and Legendre-Fourier polynomials for grazing incidence mirrors. The scatter analysis of the mirror is based on scalar scatter theory. The program accepts simple autocovariance (ACV) function models or power spectral density (PSD) models derived from mirror surface metrology data as input to the scatter calculation. The end product of the program is a user-defined pixel array containing the system Point Spread Function (PSF). The METDAT routine is used in conjunction with the OSAC program. This code reads in laboratory metrology data in a normalized format. The code then fits the data using Zernike polynomials for normal incidence systems or Legendre-Fourier polynomials for grazing incidence systems. It removes low order terms from the metrology data, calculates statistical ACV or PSD functions, and fits these data to OSAC models for the scatter analysis. In this paper we briefly describe the laboratory image testing of FUSE spare mirror performed in the near and vacuum ultraviolet at John Hopkins University and OSAC modeling of the test setup performed at NASA/GSFC. The test setup is a double-pass configuration consisting of a Hg discharge source, the FUSE off-axis parabolic mirror under test, an autocollimating flat mirror, and a tomographic imaging detector. Two additional, small fold flats are used in the optical train to accommodate the light source and the detector. The modeling is based on Zernike fitting and PSD analysis of surface metrology data measured by both the mirror vendor (Tinsley) and JHU. The results of our models agree well with the laboratory imaging data, thus validating our theoretical model. Finally, we predict the imaging performance of FUSE mirrors in their flight configuration at far-ultraviolet wavelengths.

Saha, Timo T.↗
NASA NTRS1977

An altitude-dependent spacecraft charging model

A model for the altitude dependence of the hot plasma parameters responsible for the electrostatic charging of spacecraft was developed. Based upon plasma orbit theory, the directed velocity is a function of the ambient magnetic field flux density. A consequence of this approach is that while the thermal velocity distributions (assumed to be Maxwellian) of the plasma particles are independent of the magnetic field strength (and hence altitude), the particle densities increase with magnetic field strength. Thus, according to this model, while the equilibrium voltage is independent of altitude, the charging current density increases with decreasing altitude. However, the probability of such spacecraft charging decreases with decreasing altitude.

Haffner, J. W.↗
NASA NTRS1979

The reflection of impulses from a nonlinear random sea

A model of the reflection of radar impulses from the sea at near-vertical incidence is used to account for non-Gaussian ocean waves statistics. The joint probability density function (pdf), of wave height and slope, is calculated according to the theory of Longuet-Higgins (1963) on the distribution of variables in a 'weakly nonlinear' random era. The long-crested approximation is made, a Phillips wave spectrum is assumed, and the Gram-Charlier series is truncated after skewness terms. It is found that the height and height-slope skewness coefficients bear the ratio 1:2 and that the derived impulse response and conditional cross section versus wave height are in excellent agreement with previous observations. Finally, it is suggested that the empirically determined and theoretically predicted sea state bias be corrected for in the routine processing of satellite radar altimeter data.

Jackson, F. C.↗
NASA NTRS1983

Diffusive separation of binary mixtures of CO2-H2 in a sonic-orifice expansion

The separation of binary gas mixtures of carbon dioxide and hydrogen in sonic-orifice-generated free jets is investigated over a source Reynolds number range of 100 to 3000 using the well-known electron beam fluorescence technique. The lighter species, hydrogen, is chosen as the minor species in order to examine the extent of the validity of Sherman's first-order diffusive separation theory for large separation. The diffusive separation of mixtures containing approximately 2, 5, and 20 percent hydrogen in carbon dioxide is investigated by experimentally determining the relative number densities of the two species as a function of centerline axial distance within the free jets. Sherman's diffusive separation theory is applied to the jets using axial Mach number profiles which were a combination of experimental and analytical results for gamma = 1.40 expansions. The gamma = 1.40 expansion is shown to approximate the CO2-H2 expansion quite well, and the calculated separation agrees remarkably well with the experimentally determined values.

Mccay, T. D.↗
NASA NTRS1994

Electric field effects on a near-critical fluid in microgravity

The effects of an electric field on a sample of SF6 fluid in the vicinity of the liquid-vapor critical point is studied. The isothermal increase of the density of a near-critical sample as a function of the applied electric field was measured. In agreement with theory, this electrostriction effect diverges near the critical point as the isothermal compressibility diverges. Also as expected, turning on the electric field in the presence of density gradients can induce flow within the fluid, in a way analogous to turning on gravity. These effects were observed in a microgravity environment by using the Critical Point Facility which flew onboard the Space Shuttle Columbia in July 1994 as part of the Second International Microgravity Laboratory Mission. Both visual and interferometric images of two separate sample cells were obtained by means of video downlink. The interferometric images provided quantitative information about the density distribution throughout the sample. The electric field was generated by applying 500 Volts to a fine wire passing through the critical fluid.

Zimmerli, G.↗